Is the Hadith: "There is no man who greets me except that Allah returns my soul to me so that I may return his greeting," specific to greeting at the grave, or does it include greeting in the Tashahhud and other places? And does "Allahumma salli wa sallim ala Muhammad (O Allah, bestow Your prayers and peace upon Muhammad)" fall under this Hadith?

First: A Muslim's greeting of peace (salaam) upon the Prophet, may Allah's peace and blessings be upon him, is answered by him. This is not exclusive to those who stand at his grave, but rather it is general from any place, due to the Prophet's saying: "There is no one who greets me with peace but Allah returns my soul to me so that I may return his greeting." And his saying: "Indeed, Allah has angels who travel the earth and convey to me the greetings of peace from my Ummah." The Prophet forbade taking his house as a place of celebration ('Eid) or his grave as a place of celebration ('Eid), and he informed us that our prayers reach him wherever we are.

Second: Responding to the greeting of peace is specific to the greeting, but the blessings (salat) also reach the Prophet, may Allah's peace and blessings be upon him, and both are combined, due to the Almighty's saying: "Indeed, Allah and His angels send blessings upon the Prophet. O you who have believed, ask [Allah to confer] blessing upon him and greet him with [submitting] salutation."